Coordination of non-directional overcurrent relays and fuses in active distribution networks considering reverse short-circuit currents of DGs

The main protection equipment in radial distribution networks are non-directional overcurrent relays (NDOCR) and fuses which are coordinated using the conventional protection coordination method. By installing distributed generations (DGs) in the network, reverse short-circuit currents (SCC), injected from DGs, can lead to false tripping of NDOCRs and false melting of fuses. In the previous studies, some methods have been proposed to overcome these issues using directional overcurrent relays, fault current limiter, and adaptive methods that relay on communication. The present paper proposes a new coordination method to prevent these issues without the need for installing a new equipment, by proposing a new set of selectivity constraints. Here, selectivity between equipment is established, and false tripping and false melting issues are mitigated. The coordination of protection equipment according to the proposed method requires the use of optimization algorithms, and therefore, the proposed method is formulated as a mixed-integer linear programming method to take advantage of mathematical optimization algorithms. The proposed coordination method is applied to a real distribution network and the results indicate the high efﬁciency of the proposed method in dealing with false relay tripping and fuse melting issues.

and dual setting characteristic [16,17] are examples of new characteristic curves proposed for enhancing protection coordination. The mentioned protection schemes do not use the available protection equipment on the distribution network. Therefore, the implementation of these schemes requires the design of a new protection system and construction of new equipment.
Various sources can cause false tripping issues like the contribution of induction motors to SCC in industrial networks [18], and reverse SCC injected by DGs in active distribution networks [15]. Since the location and the size of the DG can affect the false tripping issue, DGs can be allocated in such a way that false tripping can be eliminated [19]. The method, in [5], determines the size and location of FCLs in addition to the settings of the equipment considering anti-false melting and anti-false tripping constraints. These constraints are proposed such that NDOCRs and fuse are coordinated in such a way that pickup current setting (PCS ) of NDOCRs and minimum melting current of fuse (MMC ) of fuses are larger than the maximum reverse SCCs seen by NDOCRs and fuses. In [15], other settings in addition to PCS are obtained for the NDOCRs on healthy feeders such that their operating times (OTs) for reverse SCCs injected by DGs are larger than the OT of primary NDOCR at the faulty feeder. In [18], a coordination method based on a dynamic model of OC relays is proposed in order to prevent the false tripping issue caused by the contribution of induction motors to the SCC in industrial networks.
False tripping of NDOCRs and false melting of fuses are the main impacts of installing DGs on the protection coordination, many attempts have been devoted to consider them, in the previous studies. The aim of this paper is proposing a coordination method to overcome these issues by defining and adding new selectivity constraints to the conventional constraints (relay-relay, relay-fuse, fuse-relay and fuse-fuse) without the need for installing new costly equipment in the network. The conventional protection coordination method for radial distribution network is based on the coordination of the protective devices one by one from downstream to upstream. But, due to the new set of selectivity constraints, an optimization method is required to solve the proposed protection coordination algorithm. Therefore, the new method is formulated based on Mixed Integer Linear Programming (MILP) optimization algorithm, due to its advantages such as high optimality of results and high solving speed. In the previous studies, the coordination of OC relays has been pre-FIGURE 1 Typical radial distribution network sented using MILP. In this paper, the algorithm is developed to consider fuse equations and the non-linear equations for the coordination of NDOCRs and fuses are linearized to be solved in the MILP-based protection coordination algorithm. The new method is applied on a real radial distribution network and the results are compared with the results of previous methods. The contributions of this paper have been listed as below: -Presenting a new coordination method for preventing false tripping of NDOCRs and false melting of fuses without using additional equipment -Linearizing the proposed method for solving with MILP approach The structure of the paper is as follows: Section 2 describes the problem statement and proposed coordination method. In Section 3, the proposed coordination method is formulated based on MILP. Simulation results are presented and analysed in Section 4. Section 5 draws the conclusions.

PROBLEM STATEMENT AND PROPOSED METHOD
A comparison of various protection schemes for a distribution network in the presence of DGs can be seen in Table 1. A passive distribution network is shown in Figure 1. In the event of a fault, only overcurrent protection equipment located upstream of the fault can sense the SCC. Also, all SCCs pass through the equipment in a forward direction. In this case, considering selectivity constraints between the operation of backup fuse and primary fuse in (1), backup NDOCR and primary fuse in (2), and backup NDOCR and primary NDOCR as (3) would be enough for the coordination of overcurrent protection equipment. Using only these constraints for designing an overcurrent protection scheme is denoted as the 'conventional coordination method' in this paper. The coordination constraints for the OC relays and fuses are presented in [5] and [32].
The selectivity constraints given in (1)-(3) are valid for active distribution networks, however, they are not sufficient for addressing reverse SCCs injected by DGs. Figure 2 demonstrates SCCs injected by multiple sources in an active distribution network for SCs in various protection zones. SCC passing through equipment, not located at the upstream of the SC, and SCC passing through the overcurrent protection equipment in the backward direction impose major protection coordination issues. During these short-circuit (SCs), there is a possibility that the injected reverse SCCs from DG1 and DG2 cause false melting and false tripping of fuses and NDODRs.

False fuse melting
This issue is presented and highlighted considering the false melting of fuses for a fault in the protection zone of relays and other fuses. Figure 3 shows the false melting of fuse F7 before the operation of relay R5 for a SC in z R5 because of the reverse SCC of DG1 (Δt con = MMT con F 7 (I R F 7 (z R5 )) − t R5 (I P R5 (z R5 )) ≤ 0). To avoid this issue, it is suggested that new selectivity constraints given in (4) be added to the conventional constraints given in (1)-(3). Establishment of constraint (4) guarantees that the minimum melting time (MMT ) of the fuse which senses the reverse SCC is greater than the OT of primary NDOCR for a SC occurring in the relay's protection zone. According to Figure 3, using the proposed constraints, fuse F7 acts later than R5 for a SC in z R5 by considering the selectivity constraint (4), and as a result, the false melting of F7 is mitigated. Figure 4 shows the operation of F7 and F8 for SC in z F 8 . It is clear that if FT of F7 is set based on the conventional method, F7 melts before clearing the SC by F8 (Δt con = MMT con F 7 (I R F 7 (z F 8 )) − MC T F 8 (I P F 8 (z F 8 )) ≤ 0). The false melting of fuse for a SC in the protection zone of another fuse can be prevented by adding a new selectivity constraint given in (5) to the pre-existing selectivity constraints. This

FIGURE 3
Resolving false melting of F7 before the operation of R5 for SC in z R5

FIGURE 4
Resolving false melting of F7 before the operations of F8 for SC in z F 8 constraint guarantees that the MMT of the fuse, experiencing reverse SCC, is greater than the MCT of the primary fuse. As can be seen in Figure 4, the false melting issue is mitigated considering the proposed constraints for F7. Figure 5 demonstrates the false tripping of R4, using the setting obtained which uses the conventional method, where R4 clears the fault before R5 and F8 for SC in z R5 and z F 8 . As can be seen, R4 operates faster than R5 and F8 for SCs in their protection zones. Adding new selectivity constraints given in (6) and (7) to the previous constraints can guarantee and mitigate the false tripping of NDOCRs. Constraints (6) and (7), respectively, illustrate that OT of the NDOCR which senses reverse SSC must be greater than OT of the primary NDOCR or MCT of primary fuse given an SC occurs in its protection zone. As can be seen in Figure 5, the obtained protective device settings using the new constraints in (6) and (7) mitigate the false tripping of R4.

Proposed coordination method as an optimization problem
In conventional radial distribution networks, the coordination of OC equipment can be achieved without the need for using FIGURE 5 Resolving false tripping of R4 before the operation of (a) R5 for SC in z R5 and (b) F8 for SC in z F 8 an optimization algorithm. But in the proposed method, establishment of the proposed selectivity constraints for avoiding the false melting of fuses and the false tripping of NDOCRs should be achieved by optimization algorithms. Hence, (8a) is considered as the objective function (OF) of the optimization problem which contains the sum of MCT of fuses for maximum SCC and OT of NDOCRs for maximum and minimum SCCs occurring in their own protection zones. Also, constraints of the optimization problem are mentioned in (8b)-(8 g).
Subject to:

FORMULATION OF PROPOSED COORDINATION METHOD BASED ON MILP
In order to achieve the benefits of mathematical optimization algorithms, and therefore, solve the proposed coordination problem by MILP, MMT and MCT of the fuse for various FT s, and OT of NDOCR for various TMS s, PCS s and RT s are reformulated and modelled with linear formulations.

Linearization of MMT and MCT of fuse
All possible FT s of fuse i are stored in FT i as (9), and the corresponding binary variable for each FT is defined as x fus i . If x fus i,g is equal to one, gth type of fuse i will be selected. Since only one FT must be selected for each fuse, equality constraint (10) should be considered.
MMT and MCT of fuse i are defined as (11) and (12), respectively. MMT (F T i,g , I f ) and MCT (F T i,g , I f ) are constant values and demonstrate melting and clearing time of fuse i with type F T i,g and SCC equal to I f .
Therefore, l binary variable for fuse i must be considered as given in (13).

Linearization of OT of NDOCR
All possible combinations of discrete values of PCS , and various RT s for NDOCR i are stored in the PT i , and one corresponding binary variable is assigned in x rel i for each combination as shown in (14). For instance, binary variable x rel i,h corresponds to j th discrete value of PC S i and k th type of RT i ; and these settings are chosen as optimal settings of NDOCR i when of x rel i,h is equal to one. The equality constraint (15) guarantees that only one combination is chosen as an optimal setting for NDOCR i. The OT of NDOCR i are given in (16).
x rel It is clear from (16) that the OT of NDOCR i is not linear. In this case, the linearization method mentioned in (17) must be used. In (17), multiplication of a binary variable u and continuous variable v is replaced by a continuous linear variable V , by adding two constraints (17b) and (17c) to the pre-existing constraints.
By applying the linearization method in (17) to (16) Defined binary and continuous variables for NDOCR i are presented in (19).

Presentation of proposed method in MILP form
In the previous part, MMT and MCT of fuses and OT of NDOCRs are expressed based on linear variables. In this case, MILP can be used to solve the proposed coordination method. The OF of the MILP for the proposed coordination method is highlighted in (20a), and the constraints (20b-20h) are a converted form of selectivity constraints (1-7). Equations (20i-20l) are constraints added because of the linearization process. bp1, bp2 and bp3 are pairs of backup and primary equipment for coordination of fuse-fuse, relay-fuse and relay-relay, respectively. rp1 and rp2 are pairs of fuse-relay and fuse-fuse used for avoiding the false melting of fuses; and, rp3 and rp4 are pairs of relay-relay and relay-fuse used for avoiding the false tripping of NDOCRs. , and are constant values and are obtained from (11), (12) and (16). Figure 6 shows the flowchart of the proposed coordination algorithm using MILP.

SIMULATION RESULTS
The proposed coordination method is applied to the 20 kV Sirjan distribution network located in Iran. This network consists of two main feeders fed by a 63/20 kV substation, containing 125 branches and 77 residential, industrial and commercial loads. This network has been simplified as a 19 bus network in Figure 7 [19], where four SDGs with capacities of 6, 3, 4 and 5 MVA are assumed to be installed. Transient reactances of these SDGs are 0.1, 0.12, 0.11 and 0.09 p.u, respectively [33]. OC protection of this network includes 6 NDOCRs and 12 fuses. bp and rp matrices of this network are mentioned in (21). Minimum amounts of pickup current settings (PCS s) for 6 NDOCRs are 400, 150, 250, 125, 50, 150 and 50 A, respectively. It is considered that PCS s of NDOCRs can be increased up to four times of minimum amounts in steps of 0.1. Available RT s and FT s are listed in Tables 2 and 3, respectively [34].

Comparison between the proposed and conventional method
The obtained settings from the conventional method (not considering new constraints) and the proposed method (conventional constraints in addition to new ones) considering 16 cases including connection or disconnection of DGs are listed in Table 4. The mentioned time differences in Tables 5 and 6 are differences between the melting time of fuses (MM T r ) and OT of NDOCRs (t r ) for reverse SCCs with clearing time of primary fuses (MC T m ) or OT of primary NDOCRs (t m ) for maximum SC occurring in the primary equipment protection zones. In the conventional method, the coordination of protection devices is considered without the false trip impact of DGs, so the constraints (1)-(3) are only considered and solved by both MILP and GA. As can be seen from Table 4, the OF of the proposed method is larger than that of the conventional method. However, the false melting and the false tripping issues have been resolved. Referring to Tables 5 and 6, all operating time differences for the proposed method are positive amounts, therefore, the proposed method is capable of mitigating the false melting and the false tripping issues. Figure 8 demonstrates the operation of F10, R5 and F9 for maximum three-phase SC occurring in z F 10 . It can be seen that F9 and R5 with the settings obtained from the conventional

Comparison of proposed method with methods relying on FCL
In [5][6][7], a method based on installing FCL has been presented to decrease the forward and reverse SCCs to acceptable ranges.       Table 7 shows the maximum reverse SCC seen by the protective equipment before and after the installation of FCLs, and the optimal settings using the method of [7] and the proposed method, respectively. The settings of the relays and fuses and the values of the OF are shown in Table 8. As can be seen, only the settings of the two relays R5 and R7 have changed. For this approach, the addition of a FCL is required and thus the capital costs are high.
In the method presented in [5], by decreasing the SCCs and observing the constraints in (22) and (23), it is shown that the false melting and the false tripping issues can be mitigated. Constraint (22) suggests that FT is selected in a way that MMC of the fuse is be larger than the maximum reverse SCC seen by the fuse. In the same way, constraint (23) suggests that PCS of NDOCR is larger than the maximum reverse SCC seen by relay.

FIGURE 9
Interference of the operations of R4 and F13 for SC in z R4 according to settings of (a) proposed method and (b) FCL method [5] FIGURE 10 Interference of the operations of R4 and R7 for SC in z R4 according to settings of (a) proposed method and (b) FCL method The optimization problem is solved using the hybrid GA and linear programming (LP) method presented in [5]. Since the establishment of constraints (22) and (23) is not possible without limiting the injected SCC of DGs (reverse SCCs of equipment), four FCLs with impedances of 44.74, 83.17, 91.12 and 53.68 Ω are installed in series with the DGs. The result shows that the size of FCLs obtained from the method of [5] are lower than that of the method of [7]. Table 7 shows the reverse SCC in the protective equipment after the FCL installation as presented in [5]. According to Table 8, OF of FCL method is larger than that of the proposed method and it means that the sensitivity of the protection system will be reduced by installing FCL. On the other hand, the proposed method may avoid the false melting and the false tripping issues without installation of FCL, and has an OF that is lower than that of the FCL method. Therefore, the sensitivity of the protection system using the settings of the proposed method will be greater than that of the FCL method. Figures 9 and 10 show how the false melting of F13 and the false tripping of R7 for maximum three-phase SC in z R4 are solved using the proposed method and FCL method, respectively. The FCL method prevents the false melting and the false tripping issues by selecting MMC of F13 and PCS of R7 to be greater than their maximum reverse SCCs, and decreasing the maximum reverse SCC of F13 and R4, respectively, from 846 to 188 A ( Figure 9) and from 628 to 80 A ( Figure 10) by FCLs. However, it is obvious that the proposed method prevents the false melting and the false tripping issues only by correction of the equipment's settings and without any changes in SCCs. Therefore, the proposed method from the cost perspective and implementation capability is better than the FCL method.

Solving the proposed coordination problem using intelligent optimization algorithms
The proposed coordination problem with OF as (8b) and optimization constraints as (8b-8g) can be solved by intelligent optimization algorithms. Table 9 lists the OF and simulation time (ST) by solving the proposed coordination problem using the firefly algorithm (FA), PSO, SOS, BBO, cuckoo search algorithm (CSA), grey wolf optimization (GWO), imperialist competitive algorithm (ICA), GA, and teaching learning-based optimization (TLBO). It is concluded that the MILP approach reaches the minimum OF with less computational time. Therefore, this result shows the superiority of the proposed method based on MILP for solving the coordination problem.
It is worthy to note that the computational time is also dependent on the system size as well as the number of protective relays and thus the proposed MILP method could be an effective approach for large-scale systems.

The comparison of the proposed method with previous methods
The comparison of the conventional method, the FCL methods [5] and [7] and the proposed method using GA and MILP can be seen in Table 10. According to Table 10, although the OF of the conventional method is less than other methods, there are several relay false trips and fuse false blowing issues using the conventional method with both GA and MILP. Using the FCL methods can eliminate the protection problems caused by DG but with high capital costs due to FCL installation (methods of [5] and [7]). The result shows that, the proposed method solves the relay false trip and fuse false blowing issues without the need for new equipment. Due to the reduction of SCC in using FCL methods, the OF in these methods has increased. Intelligent methods based on iteration have a much higher computational time than mathematical methods such as MILP. Also, the value of the OF in the MILP method is less than the other methods.

The effect of increasing DG penetration on the proposed method
The DG penetration for the network under study has been selected in such a way that 40% of the loads can be fed by four SDGs with capacities of 6, 3, 4 and 5 MVA. However, additional case studies have been conducted considering various DG penetration levels and the results are listed in Table 11. As can be seen, as long as the DG penetration is less than 75%, the proposed method performs effectively, but at higher DG penetration levels, the proposed method has some limitation in maintaining proper protection coordination. In such a case, the combination of the proposed method and the method of using FCL can be an effective solution as seen in Table 11 for systems with significantly high penetration levels.

TABLE 10
The comparison of the conventional method, the FCL using methods [5,7]